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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 4
por William Findlay Shunk - 1880 - 318 páginas
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Mathematical tables for trigonometrical, astronomical, and nautical ...

Henry Law - 1884
...or, the logarithm of the nthpowerof m, is equal to n times the logarithm of m. PROPOSITION P THEOREM. The logarithm of any root of a number, is equal to the logarithm of that number, divided by the exponent of the root. Let X = logj, m, then m = 6X ; let the square root...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1885 - 512 páginas
...indicated by r, of both members of (4), we have whence, by the definition, - = log \?m. (9.) That is, the logarithm of any root of a number is equal to...logarithm of the number divided by the. index of the root. The preceding principles enable us to abbreviate the operations of multiplication and division, by...
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The Field Engineer: a Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - 1886 - 325 páginas
...the mixed number 74.103 lies between 10 and 100; hence its logarithm lies between 1 and 2, as does the logarithm of 74. 5. The logarithm of the product...logarithm of the number divided by the index of the root. 6. The preceding principles enable us to abridge labor in arithmetical calculations, by using simple...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1886 - 199 páginas
...the seventh power of 0.8952. В EVOLUTION BY LOGARITHMS. 15. It is proved in Algebra, Art. 399, that the logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. Hence, to extract the root of a number by logarithms,...
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College Algebra: For the Use of Academies, Colleges, and Scientific Schools ...

Edward Albert Bowser - 1888 - 540 páginas
...log m ; then m = a*. Therefore m" = (a1)" = a** ; whence by definition, log mp = px = p log m. (7) The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. For let x = log m ; then m = a1. 1 1 X Therefore m? = (a*)~r = ar ; whence by definition, 1 x 1 log(m')...
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A Course in Algebra: Being Course One in Mathematics in the ..., Parte1

Charles Ambrose Van Velzer, Charles Sumner Slichter - 1888 - 216 páginas
...Consequently nf=af*. Therefore, by definition, \og,,nf=pr That is, logan>=p log,,«. (c) 10. THEOREM. The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. Let n be any number, and let loga n—x. Then, by definition, n=a* . Consequently v/«=a?. Therefore,...
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The Normal Elementary Algebra: Containing the First Priniples of the Science ...

Edward Brooks - 1888 - 336 páginas
...nth power, B"XIll = AT". Whence, log Jl/" = nxm. Or log M" = nx log if. PRIN. 6. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, let m = log M. Then, . B™ = M. Taking nth root, E* = M *. Whence, logJHA=-. 71 or k if *_!**;...
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A High School Arithmetic (Wentworth & Hill's Practical Arithmetic)

George Albert Wentworth - 1888 - 362 páginas
...x 0.4771 = 5.2481. 413. As logarithms are simply exponents, therefore (§ 381), The logarithm of a root of a number is equal to the logarithm of the number multiplied by the index of the root. Thus, log 2* = Joflog2 = Jx0.3010 = 0.0753. log .002* = J of (7.3010...
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University Algebra: Embracing a Logical Development of the Science with ...

Charles Davies - 1889 - 320 páginas
...both members of ( 3 ), denoted by r, we have, Whence, by definition, * = Log ym . . . . (S.) That is, the logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. The applications of the above principles require a table of logarithms. A TABLK OF LOGARITHMS, is a...
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A College Algebra

James Morford Taylor - 1889 - 363 páginas
...the number multiplied by the exponent of the power ; and the logarithm of any root of a number equals the logarithm of the number divided by the index of the root. 307. From the principles proved above, we see that by the use of logarithms the operations of multiplication...
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